On the number of topologies on countable skew fields

V. I. Arnautov ; G. N. Ermakova

Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2020), pp. 63-74

Résumé

If a countable skew field $ R $ admits a non-discrete metrizable topology $ \tau _0 $, then the lattice of all topologies of this skew fields admits: – Continuum of non-discrete metrizable topologies of the skew fields stronger than the topology $ \tau _0 $ and such that $ \sup \{\tau _1, \tau _2 \} $ is the discrete topology for any different topologies $ \tau_1$ and $\tau _2 $; – Continuum of non-discrete metrizable topologies of the skew fields stronger than $ \tau _0 $ and such that any two of these topologies are comparable; – Two to the power of continuum of topologies of the skew fields stronger than $ \tau _0 $, each of them is a coatom in the lattice of all topologies of the skew fields.